Campos and de Mello [1]}
verified the TCC for power of cycle \(C_n^k, n\)  even and
\(2<k<\frac{n}{2}.\)  Also, they showed that one can obtain a
\(\Delta (C_n^k)+2\) -total coloring for these graphs in polynomial time. They also proved that \(C_n^k\)  with \(n\cong 0 \mod {(}\Delta (C_n^k)+1)\)  are
type-I and they proposed the following conjecture.
